Aaaaawww... I feel for you. She might be letting go. 11 is pretty old for a chicken, and I bet she had a wonderful life!
My RSL is 10, and I don't even want to think of that yet, but I need to. I lost her buddy about three months ago, but Red is as ornery as every with a RSL new friend. I picked up an almost full grown RSL because she was so lonely all by herself.
My Barred Rock, Diva, slowly stopped eating and drinking, her energy plummeted and then she lost a lot of weight very quickly, but she kept holding on. She tried to follow Red around the yard and do chicken things, but then she would just stand there looking out into space. She eventually developed pneumonia and died very painfully. I wished I knew the signs of a chicken withdrawing from life because I would have put her down.
Have you thought about euthanasia? It might be the kindest thing to do.
Now, I have 5 new chicks, all Olive Eggers, (Cuckoo Maran over an Easter Egger) and they've helped me to move on and remember the good times with my first flock of hens. They're ready to go outside, too. It'll take a number of weeks before I can integrate them with Red and Roxanne! I've even talked myself into building a new coop and run.
I'll keep you in my thoughts and prayers. It's never easy to lose a beloved pet.